The Canadian women dropped a 14-10 decision to Russia while Wales defeated the Canadian men's team 21-14.
Edmonton's Jen Kish scored an early try for the Canadian women but Russia pulled ahead to lead 14-5 at the half. Canada mounted a late charge with Bianca Farella of Montreal adding a score but Russia held on for the victory.
Earlier, Australia beat Canada 14-10 to send the defending champions into the plate competition. Canada shut out England 24-0 in the plate semifinal before losing to the Russians for the second straight day.
"Russia are obviously a much stronger side this year," said Canadian coach John Tait. "They have been together for many months at the European Championships and elsewhere and were already match fit. A few of their larger players have really evolved.
"Saying that, I don't think we played well against them at this tournament. We gave away too much possession through kicking and we know we didn't move the ball like we can in either match against them."
Russia beat Canada 15-12 on Friday.
New Zealand won the women's Cup final with a 41-0 rout of South Africa. Samoa defeated New Zealand 26-15 in the men's Cup final.
The Canadian men's side bowed out of the Cup competition early after dropping a 19-7 quarter-final decision to Kenya. Collins Injera scored the deciding try for Kenya, his fourth of the tournament.
Canada defeated Portugal 28-12 in the plate semifinal.
Both the Canadian men and women are gearing up for the Rugby World Cup Sevens next June in Moscow. Olympic qualification for 2016 Games in Rio de Janeiro is also a future goal.
In the men's Cup final, Paul Perez scored two tries to help Samoa claim its first Dubai Sevens title.
He scored his first try after only 20 seconds and added a second three minutes later for a 12-0 lead. Ben Lam pulled New Zealand within seven points, before Samoa's Lio Lolo picked up a dropped ball from New Zealand captain DJ Forbes and ran in a long try for 19-5.
Forbes redeemed himself with a try just before halftime to close the gap to 19-10. New Zealand's Kurt Baker made it 19-15 just after halftime, but Samoa put the match out of reach when Tulolo Tulolo scored a try with less than four minutes remaining.
"It was a very exciting moment for the boys. They played very well," Samoa captain Afa Aiono said. "There are a lot of new guys on the team. They stepped up and believed they could do the job."
Aiono, who didn't play in the final after earlier being suspended for three matches for an undisclosed violation, heaped praise on Perez.
"He's been a really good player since he came into the sevens and he has a lot of input in the team," Aiono said. "He is the other most experienced guy on the team. He has done a really good job."
New Zealand coach Gordon Tietjens put the loss down to sloppy play from his side.
"We made too many mistakes," he said. "They got off to a flyer — 20 seconds into the game scoring a try. Another two tries were from mistakes. It's pretty hard to turn around a game like that. We got within four and added a little bit of extra pressure and then we made another mistake."
The event is the second leg of the International Rugby Board's Sevens World Series.
Tietjens said he is happy the team reached its second final in the first two tournaments, giving it a six-point lead over Fiji, Kenya and Samoa in the title race.
It won its 10th series title last year.
"Two second places. We are leading the World Series at the moment. It's disappointing not to win one but it's not end of the world," he said. "You could go through the entire World Series, be pretty close and not win a tournament."
Forbes said the loss hurt a little more because of his Samoan heritage.
"Half my family were cheering for Samoa, so going back there will be a little bit of bragging rights," he said. "You go back home and they will say Samoa is one-up on us and things like that. It is still a game of rugby, so any team we lose to it's disappointing."
Kenya beat France 15-12 in the playoff for third place.
Samoa beat Wales 19-7 in the quarter-finals before edging out France 12-5 following a late try. New Zealand, which finished the group stage undefeated, routed Portugal 28-7 in the last eight and Kenya 27-7 in the semifinals.
England, which won the past two Dubai tournaments, beat Spain 26-5 for the lowly Shield title after being humbled by Portugal in the group stages and losing to Argentina in the bowl quarters.
It is tied for 12th in the series with Spain. Another powerhouse, Australia, also struggled, losing to Scotland in the bowl quarters and 40-12 to England in the shield semis.
With files from The Associated Press.